PERTURBO: a new classification algorithm based on the spectrum perturbations of the Laplace-Beltrami operator

Authors:
Nicolas Courty;Thomas Burger;Johann Laurent
Affiliations:
Université de Bretagne Sud, Université Européenne de Bretagne, Valoria;Université de Bretagne Sud, Université Européenne de Bretagne, CNRS, Lab-STICC;Université de Bretagne Sud, Université Européenne de Bretagne, CNRS, Lab-STICC
Venue:
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part I
Year:
2011

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Abstract

PerTurbo, an original, non-parametric and efficient classification method is presented here. In our framework, the manifold of each class is characterized by its Laplace-Beltrami operator, which is evaluated with classical methods involving the graph Laplacian. The classification criterion is established thanks to a measure of the magnitude of the spectrum perturbation of this operator. The first experiments show good performances against classical algorithms of the state-of-the-art. Moreover, from this measure is derived an efficient policy to design sampling queries in a context of active learning. Performances collected over toy examples and real world datasets assess the qualities of this strategy.